ATAR Notes: Forum
VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: Perla on October 08, 2018, 08:22:55 pm
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Hi everyone,
I don't know what happen, less than one month before the exam and I feel completely lost. I could do things really easily and now I cannot, maybe the stress or I don't know.. Do you h ave any advice or something, I do not want to fail my exam.
Also, if someone could help me with these 2 questions please.
If Pr (E ∩ F’) = 0.4 , Pr (E’∩ F’) = 0.05 and (E ∩ F) is denoted as x, given that Pr (F | E) = 1/5
i. Find Pr (E ∪ F)
ii. Find Pr (E | F’)
Thank you
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It's best if you draw a Venn diagram for it, with E as a circle intersecting F, and a background.
Pr(E ∩ F’) would be E minus the bit that intersects with F, so that would be 0.4
Pr(E' ∩ F’) would be the background itself, and that is 0.05
Pr (F|E) = Pr(F∩E)/Pr(E) = x/Pr(E) = 1/5 so Pr(E) = 5x. Pr(E) is also 0.4+x if you look at the Venn diagram, so 5x = 0.4+x, x =Pr(F∩E) = 0.1
Pr(F) = 1-Pr(E ∩ F’)-Pr(E' ∩ F’) = 0.55 if you look at your Venn diagram again.
So that leaves us with the questions
Pr(E∪F)=Pr(E)+Pr(F)-Pr(F∩E)=0.5+0.55-0.1=0.95
Pr(E|F’)=Pr(F∩E)/Pr(F')=0.1/0.45=0.222..
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It's best if you draw a Venn diagram for it, with E as a circle intersecting F, and a background.
Pr(E ∩ F’) would be E minus the bit that intersects with F, so that would be 0.4
Pr(E' ∩ F’) would be the background itself, and that is 0.05
Pr (F|E) = Pr(F∩E)/Pr(E) = x/Pr(E) = 1/5 so Pr(E) = 5x. Pr(E) is also 0.4+x if you look at the Venn diagram, so 5x = 0.4+x, x =Pr(F∩E) = 0.1
Pr(F) = 1-Pr(E ∩ F’)-Pr(E' ∩ F’) = 0.55 if you look at your Venn diagram again.
So that leaves us with the questions
Pr(E∪F)=Pr(E)+Pr(F)-Pr(F∩E)=0.5+0.55-0.1=0.95
Pr(E|F’)=Pr(F∩E)/Pr(F')=0.1/0.45=0.222..
Not to doubt you (more I want to see if I've made an error myself), but using a Karnaugh table I actually get slightly different results (Pr(F'∩E) for me is 0.4 not 0.1). I'm also confused as to why you compute Pr (F|E) when it's not one of OP's listed questions, and define Pr(E|F’) as Pr(F∩E)/Pr(F') when I would have thought it should be Pr(F'∩E)/Pr(F'). The other thing that confuses me is that to answer both i and ii, you don't even have to touch the unknown value. Pr(E ∪ F) (which becomes 1-Pr(F'∩E')) has a numerical probability from the very beginning of 1-0.05 = 0.95, and so does Pr (E | F’)=Pr(F'∩E)/Pr(F'), with a probability of 0.4/0.45=40/45=8/9.
Ultimately, more than happy to be proven wrong, getting the right answer is more important than being 'right' :P
(https://media.discordapp.net/attachments/462874454184296448/499842855771308042/unknown.png)
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Not to doubt you (more I want to see if I've made an error myself), but using a Karnaugh table I actually get slightly different results (Pr(F'∩E) for me is 0.4 not 0.1). I'm also confused as to why you compute Pr (F|E) when it's not one of OP's listed questions, and define Pr(E|F’) as Pr(F∩E)/Pr(F') when I would have thought it should be Pr(F'∩E)/Pr(F'). The other thing that confuses me is that to answer both i and ii, you don't even have to touch the unknown value. Pr(E ∪ F) (which becomes 1-Pr(F'∩E')) has a numerical probability from the very beginning of 1-0.05 = 0.95, and so does Pr (E | F’)=Pr(F'∩E)/Pr(F'), with a probability of 0.4/0.45=40/45=8/9.
Ultimately, more than happy to be proven wrong, getting the right answer is more important than being 'right' :P
(https://media.discordapp.net/attachments/462874454184296448/499842855771308042/unknown.png)
I think the values you got were correct. It should be 0.4/0.45 and not 0.1/0.45.
Computing Pr (F|E)= 0.2 helps to work out the probability of all of 'E' which ends up being 5x when worked out algebraically.